[en] Single crystals of the mixed rare-earth orthoferrite Dy_1-xHo_xFeO₃ (x=0.25, 0.5, and 0.75) have been studied by Mossbauer spectroscopy in the 1.3-298 K temperature range. Several temperature-induced Fe³⁺ spin reorientation transitions have been observed. On cooling, a locally discontinuous reorientation from the a to the b orthorhombic axis took place near 40 K followed by a continuous reorientation from the b to the c axis. The onset temperature of the latter transition depends linearly on Ho concentration x. An x-T phase diagram of Dy_1-xHo_xFeO₃ is proposed which extrapolates well to the results of previous studies of pure HoFeO₃ and pure DyFeO₃. The continuous Fe³⁺ spin reorientation in the bc plane showed the hyperfine interactions of the ⁵⁷Fe nuclei to split into two branches. This branching is associated with different Fe unit cell positions. The temperature variation of the difference in magnetic hyperfine fields agrees well with a previous calculation of a similar effect in NMR. We also observed a new, very sharp Fe³⁺ spin reorientation from the c to the b orthorhombic axis upon cooling a Dy_1-xHo_xFeO₃ single-crystal absorber between 3 K and 2.3 R. We suggest that this transition is driven by ordering of the rare-earth spins and a microscopic mechanism is proposed. (author)